Soundness problem for Resource-Constrained Workflow nets.

Slides:



Advertisements
Similar presentations
Chapter 7: Deadlocks.
Advertisements

Completeness and Expressiveness
On 1-soundness and Soundness of Workflow Nets Lu Ping, Hu Hao and Lü Jian Department of Computer Science Nanjing University
Techniques to analyze workflows (design-time)
Partial Order Reduction: Main Idea
Part 3: Safety and liveness
Introduction to Petri Nets Hugo Andrés López
1 Analysis of workflows : Verification, validation, and performance analysis. Wil van der Aalst Eindhoven University of Technology Faculty of Technology.
A university for the world real R © 2009, Chapter 3 Advanced Synchronization Moe Wynn Wil van der Aalst Arthur ter Hofstede.
Process Models In this section, we focus on the control-flow perspective of processes. We assume that there is a set of activity labels.
Automatic Verification Book: Chapter 6. What is verification? Traditionally, verification means proof of correctness automatic: model checking deductive:
Petri Nets Section 2 Roohollah Abdipur.
Based on: Petri Nets and Industrial Applications: A Tutorial
PROTOCOL VERIFICATION & PROTOCOL VALIDATION. Protocol Verification Communication Protocols should be checked for correctness, robustness and performance,
Workflow Management Kap. 4. Analyzing Workflows Wil van der Aalst has copyrights to almost all figures in the following slideshow made by Lars Frank.
Discussion #33 Adjacency Matrices. Topics Adjacency matrix for a directed graph Reachability Algorithmic Complexity and Correctness –Big Oh –Proofs of.
On the Dynamics of PB Systems with Volatile Membranes Giorgio Delzanno* and Laurent Van Begin** * Università di Genova, Italy ** Universitè Libre de Bruxelles,
IE 469 Manufacturing Systems
Deadlocks CS 3100 Deadlocks1. The Deadlock Problem A set of blocked processes each holding a resource and waiting to acquire a resource held by another.
Synthesis of Embedded Software Using Free-Choice Petri Nets.
1 Wednesday, June 28, 2006 Command, n.: Statement presented by a human and accepted by a computer in such a manner as to make the human feel that he is.
Chapter 7: Deadlocks. 7.2 Chapter Objectives To develop a description of deadlocks, which prevent sets of concurrent processes from completing their tasks.
1 M. Bozyigit ICS Operating Systems Deadlock. 2 Deadlock n Permanent blocking of a set of processes that either compete for system resources or communicate.
/k soundness of free-choice workflow nets 1 of 10 Soundness of Free Choice Workflow Nets K.M. van Hee, M. Voorhoeve Eindhoven Univ. Tech.
Behaviour-Preserving Transition Insertions in Unfolding Prefixes
1 School of Computing Science Simon Fraser University CMPT 300: Operating Systems I Ch 7: Deadlock Dr. Mohamed Hefeeda.
02/19/2008CSCI 315 Operating Systems Design1 Deadlock Notice: The slides for this lecture have been largely based on those accompanying the textbook Operating.
Deadlock. Example Process 1 Process 2 Resource 1 Resource 2.
Silberschatz, Galvin and Gagne ©2009 Operating System Concepts – 8 th Edition, Chapter 7: Deadlocks.
*Department of Computing Science University of Newcastle upon Tyne **Institut für Informatik, Universität Augsburg Canonical Prefixes of Petri Net Unfoldings.
Proof by Deduction. Deductions and Formal Proofs A deduction is a sequence of logic statements, each of which is known or assumed to be true A formal.
Silberschatz, Galvin and Gagne  Operating System Concepts Deadlock and Starvation Deadlock – two or more processes are waiting indefinitely for.
What we will cover…  The Deadlock Problem  System Model  Deadlock Characterization  Methods for Handling Deadlocks  Deadlock Prevention  Deadlock.
Time, Clocks, and the Ordering of Events in a Distributed System Leslie Lamport (1978) Presented by: Yoav Kantor.
Deadlock Characterization
Linear and Branching Time Safety, Liveness, and Fairness
1 A Petri Net Siphon Based Solution to Protocol-level Service Composition Mismatches Pengcheng Xiong 1, Mengchu Zhou 2 and Calton Pu 1 1 College of Computing,
Jorge Muñoz-Gama Universitat Politècnica de Catalunya (Barcelona, Spain) Algorithms for Process Conformance and Process Refinement.
Soundness problem for Resource-Constrained Workflow nets revisited Natalia Sidorova and Christian Stahl.
Silberschatz, Galvin and Gagne ©2009 Operating System Concepts – 8 th Edition Deadlocks.
CY2003 Computer Systems Lecture 7 Petri net. © LJMU, 2004CY2003- Week 72 Overview Petri net –concepts –Petri net representation –Firing a transition –Marks.
Silberschatz, Galvin and Gagne ©2013 Operating System Concepts – 9 th Edition Chapter 7: Deadlocks.
Internet Software Development Controlling Threads Paul J Krause.
Cosc 4740 Chapter 6, Part 4 Deadlocks. The Deadlock Problem A set of blocked processes each holding a resource and waiting to acquire a resource held.
1 The Theory of NP-Completeness 2 Cook ’ s Theorem (1971) Prof. Cook Toronto U. Receiving Turing Award (1982) Discussing difficult problems: worst case.
Petri Nets Lecturer: Roohollah Abdipour. Agenda Introduction Petri Net Modelling with Petri Net Analysis of Petri net 2.
Silberschatz, Galvin and Gagne ©2013 Operating System Concepts – 9 th Edition Chapter 7: Deadlocks.
Modelling by Petri nets
CS6502 Operating Systems - Dr. J. Garrido Deadlock – Part 2 (Lecture 7a) CS5002 Operating Systems Dr. Jose M. Garrido.
 The Deadlock Problem  System Model  Deadlock Characterization  Methods for Handling Deadlocks  Deadlock Prevention  Deadlock Avoidance  Deadlock.
CSCI1600: Embedded and Real Time Software Lecture 11: Modeling IV: Concurrency Steven Reiss, Fall 2015.
Operating Systems (CS 340 D) Dr. Abeer Mahmoud Princess Nora University Faculty of Computer & Information Systems Computer science Department.
Process Algebra (2IF45) Basic Process Algebra Dr. Suzana Andova.
1 CS.217 Operating System By Ajarn..Sutapart Sappajak,METC,MSIT Chapter 6 Deadlocks Slide 1 Chapter 6 Deadlocks.
Deadlock A deadlock is a situation wherein two or more competing actions are waiting for the other to finish, and thus neither ever does. Example : “When.
Diagnostic Information for Control-Flow Analysis of Workflow Graphs (aka Free-Choice Workflow Nets) Cédric Favre(1,2), Hagen Völzer(1), Peter Müller(2)
Technology of information systems Lecture 5 Process management.
Process Mining – Concepts and Algorithms Review of literature on process mining techniques for event log data.
CSE Operating System Principles Deadlocks. CSE – Operating System Principles2 Overview System Model Deadlock Characterization Methods for.
Chapter 7: Deadlocks.
OPERATING SYSTEM CONCEPTS AND PRACTISE
composition of workflows
Concurrency: Deadlock and Starvation
CSS 496 Business Process Re-engineering for BS(CS)
Concurrent Systems Modeling using Petri Nets – Part II
Introduction to Petri Nets (PNs)
Wil van der Aalst Eindhoven University of Technology
CSCI 315 Operating Systems Design
CENG334 Introduction to Operating Systems
Chapter 7: Deadlocks.
Presentation transcript:

Soundness problem for Resource-Constrained Workflow nets

Resource-Constrained WF-nets (RCWF-nets) Resource places P r Production net N p with production places P p P r  P p =  A Petri net N with a set of places P p  P r is an RCWF-net if its projection on P p is a workflow net. i f

Mixable instances vs. independent instances Instances in the production net can be independent, e.g. as in handling insurance claims Or they can interfere with each other: produce a number of bicycles, all exactly the same, no matter which wheels go to which one… For independent instances, we can introduce token id’s, and further reduce the model to classical Petri nets by substituting the production net by a state machine obtained from the reachability graph of the production net. So in both cases we can just deal with classical Petri nets

Different types of resources Durable: machines, people Consumable: paper, building materials, etc. Producible: whatever you produce in your process We will focus on durable resources only They get involved in the process when executing some tasks and then get released When all instances terminate, it’s logical to expect that all resources are back

Resource or not?

At any moment of time, the amount of resources cannot exceed the initial amount of them.

Soundness for RCWF-nets An RCWF-net N is (k,R)-sound if for any marking m reachable from the initial marking k[i]+R, marking k[f]+R is reachable and m r < R N is k-sound if there is an R such that N is (k,R’)-sound for all R’  R N is R-sound if it is (k,R)-sound for any natural k N is sound if there is an R such that N is (k,R’)-sound for any natural k and any R’  R So we parameterize on the number of instances, the number of resources, or on both. Soundness of RCWF-nets only covers the proper termination requirement

An evident necessary condition of soundness The production net of a sound RCWF-net is generalized sound, i.e. for every marking reachable from k[i], marking k[f] is reachable. For any sound RCWF-net its production net is generalized sound

Redundancy and persistency no resource place can ever obtain tokens, if it was not marked initially. every resource place should become marked again when the net terminates.

Non-redundancy criterion

Non-persistency criterion

Checking that all resources are back if terminated The net should work correctly for all “large” markings, i.e. we can always add resource tokens to make a firing sequence that is executable in the production net also executable in the RCWF-net That implies (with some extra steps) that, for every sound RCWF-net every transition invariant of the RCWF-net is a transition invariant of its production net and vice versa

Corollary The transition invariant check allows us to ensure that if all the instances of an RCWF-net terminate (tokens on f), then all the resources are back i.e. if the production net of an RCWF-net is sound and the invariant condition holds, deadlocks and livelocks can happen due to resources only

Still it can go wrong

Reducing the soundness problem to the home space problem An RCWF-net is sound iff is a home space of its transformed net. R0 resources

Checking the home space property Partition the space of the reachable markings into with The HS property holds for all markings in R’ Goal: to show that it is sufficient to check that it holds for the set F’’ of minimal markings of R’’ We partition R’’ further into and define Proof by induction on i i = 0 is trivial

Checking the home space property (2) Take. If the hs-property holds. If not, take such that Note that for some  and Then and, hence it contain at least one token on some production place, while contains none Thus

Problem solved? Well, we can check reachability on an unbounded net – in theory it is decidable, but the check was never implemented… Next to investigate: can we apply algebraic methods to solve the problem like we did for generalized soundness? It’s no way straightforward… to be continued…